A cofinality-preserving small forcing may introduce a special Aronszajn tree

Archive for Mathematical Logic 48 (8):817-823 (2009)
  Copy   BIBTEX

Abstract

It is relatively consistent with the existence of two supercompact cardinals that a special Aronszajn tree of height ${\aleph_{\omega_1+1}}$ is introduced by a cofinality-preserving forcing of size ${\aleph_3}$

Categories

Keywords

Reprint years

DOI

10.1007/s00153-009-0155-1

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,991

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Aronszajn trees and the successors of a singular cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.
Can a small forcing create Kurepa trees.Renling Jin & Saharon Shelah - 1997 - Annals of Pure and Applied Logic 85 (1):47-68.
Creatures on ω 1 and weak diamonds.Heike Mildenberger - 2009 - Journal of Symbolic Logic 74 (1):1-16.
Gap structure after forcing with a coherent Souslin tree.Carlos Martinez-Ranero - 2013 - Archive for Mathematical Logic 52 (3-4):435-447.
Specializing Aronszajn Trees with Strong Axiom A and Halving.Heike Mildenberger & Saharon Shelah - 2019 - Notre Dame Journal of Formal Logic 60 (4):587-616.
The tree property and the failure of SCH at uncountable cofinality.Dima Sinapova - 2012 - Archive for Mathematical Logic 51 (5-6):553-562.
Specialising Aronszajn trees by countable approximations.Heike Mildenberger & Saharon Shelah - 2003 - Archive for Mathematical Logic 42 (7):627-647.
The special Aronszajn tree property.Mohammad Golshani & Yair Hayut - 2019 - Journal of Mathematical Logic 20 (1):2050003.
A forcing axiom for a non-special Aronszajn tree.John Krueger - 2020 - Annals of Pure and Applied Logic 171 (8):102820.
Aronszajn tree preservation and bounded forcing axioms.Gunter Fuchs - 2021 - Journal of Symbolic Logic 86 (1):293-315.

Analytics

Added to PP
2013-11-23

Downloads
25 (#653,738)

6 months
16 (#172,464)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A relative of the approachability ideal, diamond and non-saturation.Assaf Rinot - 2010 - Journal of Symbolic Logic 75 (3):1035-1065.
On the ideal J[κ].Assaf Rinot - 2022 - Annals of Pure and Applied Logic 173 (2):103055.
More Notions of Forcing Add a Souslin Tree.Ari Meir Brodsky & Assaf Rinot - 2019 - Notre Dame Journal of Formal Logic 60 (3):437-455.

View all 6 citations / Add more citations

References found in this work

Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
A new class of order types.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (3):187-222.
A very weak square principle.Matthew Foreman & Menachem Magidor - 1997 - Journal of Symbolic Logic 62 (1):175-196.
Adding a closed unbounded set.J. E. Baumgartner, L. A. Harrington & E. M. Kleinberg - 1976 - Journal of Symbolic Logic 41 (2):481-482.
A relative of the approachability ideal, diamond and non-saturation.Assaf Rinot - 2010 - Journal of Symbolic Logic 75 (3):1035-1065.

View all 7 references / Add more references